The effect of boundary conditions on Rayleigh-Taylor instability

Laser experiments are widely used to investigate excitation of Rayleigh-Tay lor modes, which are of great importance for astrophysical applications. Me asured growth rates are normally compared with either the sharp interface o r the smooth gradient model. In the present paper an analytical solution is obtained that is valid for arbitrary density gradient scale L. It is a fur ther development of the Mikaelian & Lindl model. New explicit presentation omega(k) is found which describes all discrete modes at all transverse wave numbers k with one parametric expression. A critical value of kL is shown t o exist when two independent solutions for the fastest growing main mode be come degenerate, in this case the growth rate is calculated exactly. The fo cus is on astrophysical applications when boundary conditions are at infini ty. The case of rigid walls is also considered to study the interrelation w ith the Chandrasekhar model. Results are supposed to be used for nonlinear RT treatment to analyze mixing in supernovae and other RT-driven objects.